1. Field of the Invention
The present invention relates to a rendering apparatus, a multispectral image scanner, and a three-dimensional automatic gonio-spectrophotometer. More particularly, the present invention concerns a rendering apparatus for reproducing and displaying an object three-dimensionally and realistically through image processing technique such as computer graphics, a multispectral image scanner usable in the rendering apparatus to measure a spectral reflectance distribution using optical filters, and a three-dimensional automatic gonio-spectrophotometer usable in the rendering apparatus to automatically conduct three-dimensional spectrocolorimetry of an object having complicated reflection characteristics such as fabrics.
2. Description of the Related Art
Conventionally, a method is known in which, with respect to an object in which the optical properties of the surface are uniform, the color of the object is reproduced and displayed three-dimensionally and realistically by calculating coloring on the basis of a ray tracing method by using the two-dimensional spectral reflectance factor of the object surface (A. Takagi et al., Computer Graphics, Vol. 24, No. 4, 1990).
In this method, as shown in Formula (1) shown below, color specification values (tristimulus values) of the CIE (International Commission on Illumination) standard XYZ colorimetric system are first determined on the basis of a spectral reflectance factor and the like of the object surface. These tristimulus values are then transformed into color specification values peculiar to the colorimetric system through a linear combination transform shown in Formula (2) below, are subjected to .gamma. correction, and are transformed into RGB gradients, thereby displaying a reproduced image of the object. ##EQU1## Where, R(.lambda., .PHI.): spectral reflectance factor of an object
L(.lambda., .THETA.): spectral radiance of an incident light source PA1 x(.lambda.), y(.lambda.), z(.lambda.): CIE color matching functions PA1 .PHI.: angular condition determined by an incident angle, a reflection angle, and an azimuth angle (e.g., an incident azimuth angle and a reflection azimuth angle) PA1 .THETA.: angular condition determined by an incident angle and an azimuth angle (e.g., an incident azimuth angle) PA1 .theta.: incident angle PA1 .omega.: very small solid angle as viewed from the infinitesimal area of the object surface PA1 .OMEGA.: total solid angle as viewed from the infinitesimal area of the object surface PA1 .lambda.: wavelength PA1 k: normalization coefficient ##EQU2## Where, Y.sub.R, Y.sub.G, Y.sub.B : luminance values of the RGB colorimetric system PA1 A: color-matching transformation matrix consisting of a.sub.ij (i, j=1, 2, 3) PA1 a.sub.ij : coefficient of a display unit (determined by measurement of the luminance of the display screen) PA1 R(.lambda.): spectral reflectance factor of the sample F PA1 R.sub.w (.lambda.): spectral reflectance factor of a working standard white plate C PA1 r(.lambda.): relative spectral reflectance factor of the sample F relative to the reference white plate S PA1 r.sub.w (.lambda.): relative spectral reflectance factor of the working standard white plate C relative to the reference white plate S
According to this method, it is possible to obtain the spectral radiance per very small solid angle at a time when a spectral radiance L(.lambda., .THETA.), which is made incident upon the infinitesimal area of the object surface at an angle .theta., is reflected by the object surface having a spectral reflectance factor R(.lambda., .PHI.), and is directed toward an image display position (i.e., a visual point). By integrating this spectral radiance per very small solid angle with respect to the solid angle, it is possible to obtain the total spectral radiance made incident upon the visual point from the infinitesimal area. Then this total spectral radiance is transformed into tristimulus values of the XYZ colorimetric system.
With the above-described method, however, since the spectral reflectance factor of an infinitesimal area is used, the method is applicable to an object in which the spectral reflectance distribution of the surface is uniform, but it is not applicable to an object in which the spectral reflectance distribution of the surface is nonuniform, such as an object having a fine colored pattern and texture. In addition, since the spectral reflectance differs for the object having complicated reflection characteristics, such as fabrics, depending on angular conditions for measuring the object, this method is not applicable to such an object.
In addition, to apply the above-described method to an object in which the spectral reflectance distribution of the surface is nonuniform, the spectral reflectance factor of the infinitesimal area of the object is required over the entire surface. However, since no apparatus for measuring the spectral reflectance factor for the entire surface has been available, it is impossible to obtain a desired amount of measured values. Moreover, even if such measured values were available, since it is necessary to retain the measured values for the entire object surface in accordance with the wavelengths with respect to combinations of three-dimensional angular conditions, the amount of data held becomes enormously large. Thus it is difficult to configure a practicable system.
As a method of displaying a fine colored pattern and texture on an object, a texture mapping method is known (J. F. Blinn et al., Communication of the ACM, Vol. 19, No. 10, 1976). This method enables displaying a fine pattern and texture by mapping the plane pattern onto the object surface.
As for this method, however, mapping is generally effected by using as pattern data those color specification values of the RGB colorimetric system which are measured on the basis of a three-component separation method using a color scanner or the like. Although this method is effective in displaying a colored pattern and texture on the object surface, it is impossible to display an accurately color-matched and reproduced image of the object surface. In other words, since the color specification values for mapping are values which are measured under a certain light source and are determined uniformly, the color specification values cannot be changed in accordance with a change in the spectral distribution of incident light, e.g., a change of the light source. In addition, since the RGB colorimetric system is a colorimetric system peculiar to a measuring system, transformation to another colorimetric system is complicated, and the accuracy at the time of transformation becomes low. Furthermore, since the angular conditions for measuring the color specification values are dependent on the measuring system of a measuring apparatus such as a color scanner and are therefore determined uniformly, it is impossible to obtain color specification values at arbitrary angular conditions.
In addition, in the measurement of the aforementioned spectral reflectance distribution, a method has been proposed in which an apparatus for detecting reflected light by using a scanner is provided, and the spectral reflectance in infinitesimal areas is estimated from a color-separation output system for image plane pixels by using this scanner (Mitsugu Nakayama, et al., "Estimation of spectral reflectances for color scanners", Journal of the Color Science Association of Japan, Vol. 14, No. 1, 1990).
In this method, the spectral reflectance is estimated on the basis of outputs for respective channels (hereafter referred to as channel outputs) of a scanner using interference filters for predetermined wavelength bands (hereafter referred to as channels), i.e., a limited number of narrow-bands. According to this method, overall characteristics including all the characteristics of a scanner optical system such as those of a light source, optical filters, a light-detecting element, and the like are determined by using a plurality of samples whose spectral reflectances are already known. By applying these characteristics to measured values of a sample whose reflectance is unknown, the spectral reflectance can be estimated.
In addition, as similar methods, a method proposed by Stephen K. Park et al. for determining the overall characteristics (Applied Optics, Vol. 16, No. 12, 1977) and a method proposed by Maloney (Journal of the Optical Society of America A Vol. 3, No. 10, 1986) are also known. In the method proposed by Stephen K. Park et al., the spectral reflectance is estimated by applying the Shannon's data-sampling theorem to channel outputs which are not necessarily narrow-bands. Meanwhile, in the method proposed by Maloney, it is assumed that the spectral reflectance can be expressed by the weighted linear sum of channel outputs, and the spectral reflectance is estimated by the method of least squares.
In each of the above-described methods, however, since the bandwidths of the filters used are relatively wide, the spectral reflectance is estimated from a small number of channel outputs on condition that the spectral distribution of the light source and the spectral sensitivity of the light-receiving element in the scanner optical system are smooth. In these methods, there are problems in that numerous measurements and complicated calculations are required, and that when optical conditions have changed, resetting must be carried out in a similar procedure.
In a scanner which uses a CCD line sensor as the light-detecting element, a fluorescent lamp is frequently used as a line light source. However, since a bright line spectrum corresponding to the component of a sealed gas is produced from this fluorescent lamp, the spectral distribution is not smooth. Hence, errors occur in those methods with a premise that the spectral characteristics are smooth, as described above.
Furthermore, although the measurement of colors of light, paint and the like is conventionally carried out for the quality control of paints and the like, there has been no apparatus for properly conducting the colorimetry of the surface of a sample with a complicated shape in which the quantity of light and the degree of color change depending on the light-detecting direction, such as a fiber or metallic coating, i.e., for conducting the three-dimensional measurement of the spectral reflectance factor of an object.
Meanwhile, as apparatuses which are capable of conducting the colorimetry of such an object, photometers including a colorimeter for measuring the color of an object and a color meter are known. Among these photometers, a photometer, such as a two- or three-dimensional automatic gonio-spectrophotometer, is known for determining the reflectance not merely by uniformly conducting colorimetry at a position for measuring a sample, but by changing angles such as the incident angle and the light-detecting angle, i.e., the angle of direction of light to be detected with respect to the sample.
In this two-dimensional automatic gonio-spectrophotometer, as shown in FIG. 35A, the changing of the incident angle .theta. from the light source and the light-detecting angle .phi. to the light-detecting element, which are determined by angles formed with respect to the normal line of the surface of a sample F, is controlled by a personal computer having a central processing unit (CPU) so as to measure the spectral reflectance factor of the sample.
However, in the angle change control of such a two-dimensional automatic gonio-spectrophotometer, since the measurement is performed by fixing a detector unit (not shown) and by changing the incident angle .theta. and the light-detecting angle .phi. by rotating a light source unit 600 and a sample base 604, it is impossible to determine the spectral reflectance factor three-dimensionally.
In contrast, as shown in FIG. 35B, in a three-dimensional automatic gonio-photometer, which is provided with a three-dimensional angle-changing mechanism for manually rotating the sample F, the light source unit (not shown) is fixed, and the luminous intensity is measured three-dimensionally by changing the angles by rotating the sample F, a detecting unit 602, and the sample base 604.
However, with this three-dimensional automatic gonio-photometer, since only the reflection intensity of the sample F is determined, it is impossible to conduct spectrophotometric colorimetry through the measurement of the spectral reflectance. To conduct this spectrophotometric colorimetry, it is sufficient to dispose a spectroscope or the like. Yet, since a movable section of the three-dimensional automatic gonio-photometer is located in the detecting unit 602 for measuring the quantity of light, it is difficult to dispose a large-size optical instrument such as the spectroscope in this movable section.
Accordingly, the three-dimensional spectral reflectance factor of the sample F has been determined by estimating on the basis of measured data obtained by a two-dimensional automatic gonio-spectrophotometer and measured data obtained by a three-dimensional automatic gonio-photometer.
However, in determining the three-dimensional measured data of the spectral reflectance factor from the aforementioned measured data obtained by the two-dimensional automatic gonio-spectrophotometer and measured data obtained by the three-dimensional automatic gonio-photometer, there have been problems in that much time and labor are required, and that error is unavoidable since the resultant data are based on the estimation.
In addition, the spectral reflectance factor R(.lambda.) is determined from a ratio between a spectral radiant flux with a wavelength .lambda. reflected from an object and a spectral radiant flux with the wavelength .lambda. reflected from a perfect reflecting diffuser (JIS-Z8105, Z8722). To determine the spectral reflectance factor in a shorter period of time, a double beam method is known in which, by using a reference white plate S such as a glass plate coated with barium sulfate, the spectral reflectance factor is determined on the basis of measured values of reflected light from the reference white plate S and reflected light from the sample F. In this double beam method, light emitting from the same light source can be radiated to both the reference white plate S and the sample F under the same conditions, i.e., with an identical incident angle and an identical light-detecting angle, and the spectral reflectance factor can be determined on the basis of the following Formula (a): EQU R(.lambda.)=R.sub.w (.lambda.).multidot.r(.lambda.)/r.sub.w (.lambda.)(a)
Where,
However, a phenomenon (sheen) is known in which, if the reference white plate S is used, even though a surface may be uniformly diffusive in an area with a small incident angle, a peak of strong reflected light appears in the direction of regular reflection (in which the incident angle .theta. and the light-detecting angle .phi. are substantially identical) when the incident angle becomes large. In this area of sheen, uniform diffusion becomes nonuniform, so that a method for accurately determining the spectral reflectance factor in such an area of sheen has not been established.